C₂×#20267913 #27204040

order	13184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#20267913

Splittings

Sylow

C₁₀₃ ⋊ C₂×#444

Subgroups

	subgroup	G/H
center	C₂×C₄	D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₃
Fitting, prime radical	C₂×#135×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₄×D₄
cosocle	C₂×C₄×C₁₀₃	C₂⁴
hypercenter	C₂×#135	D₁₀₃
hypocenter	C₁₀₃	C₂×#444
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 4 generators on 121 points:

(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(106,109,110,117,111,118,115,119)(107,112,114,121,108,116,113,120);(106,108)(107,111)(109,116)(110,113)(112,118)(114,115)(117,120)(119,121);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(106,107,110,114,111,108,115,113)(109,116,117,120,118,112,119,121);(104,105)

Conjugacy classes & character table

1472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 13406);

C2×#20267913 #27204040